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Analytical and Bioanalytical Chemistry (v.364, #5)
4th Symposium on Mass Spectrometric Methods for Element Trace Analysis
by Klaus G. Heumann (pp. 365-366).
New developments and applications in GDMS by A. Bogaerts; R. Gijbels (pp. 367-375).
An overview is given about the new developments in GDMS, both with respect to the glow discharge source as to the coupling with various kinds of mass spectrometers. Moreover, as for every analytical technique, methodological and fundamental research is being carried out to improve the analytical results of GDMS, and some of the new developments in these fields will be discussed as well. Finally, the various analytical applications of GDMS will be presented.
Determination of Y, Zr and ultra-low Nb concentrations in geological material by multi-ion counting spark-source mass spectrometry (MIC-SSMS) by J. A. Pfänder; K. P. Jochum; A. Sassen; B. Stoll; P. Maissenbacher; M. Murmann (pp. 376-380).
Precise concentrations of Zr, Y and Nb in the μg/g to ng/g range have been determined in rock samples using multi-ion counting spark-source mass spectrometry (MIC-SSMS). A high resolution method, combined with interference correction on 91Zr and 93Nb for low concentration samples, was applied. An analytical precision of 2–5% for concentrations down to 0.020 μg/g and 10% for lower concentrations was attained. The detection limit is below 0.005 μg/g. By measuring international reference materials, the accuracy of the method was determined to be within about 10% of the recommended values. However, the accuracy of the final concentration is influenced by interference corrections, but the additional error is below 20%. The interference problem is most difficult for Al-rich samples (>15% Al2O3), as the interfering molecules are 40Ca27Al12C2 + and 27Al3 12C+. The accordance between ICP-MS and MIC-SSMS results is worse for low Nb concentrations in the ng/g range. Here, ICP-MS gives systematically lower values than MIC-SSMS. The reason for this discrepancy is not yet clear, but may be caused by Nb loss during chemical treatment of the samples prior to ICP-MS measurements.
MIC-SSMS analyses of eight new geological standard glasses by Brigitte Stoll; K. P. Jochum (pp. 380-384).
To obtain suitable geological reference materials for microanalytical purposes, a set of eight natural glasses was prepared by direct fusion of rock chips. Multi-ion counting spark source mass spectrometry (MIC-SSMS) has been applied for trace element analysis of these reference materials. The overall analytical uncertainty of the MIC-SSMS results was determined by considering 14 possible sources of errors. It generally ranges between < 2–7% depending on the element and its concentration. Nearly all MIC-SSMS data agree with the reference values within 0–10%, indicating that the estimate of the overall analytical uncertainty is reasonable.
Applications of ICP-MS in semiconductor industry by M. Horn (pp. 385-390).
Contamination in semiconductor industry is a very serious drawback during the production of integrated circuits. Connected with the ongoing miniaturization smaller and smaller amounts of metal contamination can effect the integrated circuits. Because of the outstanding detection limits ICP-MS is widely spread in semiconductor industry. The main applications are metal and semi-metal analysis in deionized water, chemicals and on the wafer surface. The challenges in semiconductor industry are the required detection limits, which are mainly limited by contamination during sample treatment and the background of the instruments.
Methods for boron analysis in boron neutron capture therapy (BNCT). A review by Thomas U. Probst (pp. 391-403).
The possibilities and limitations of the numerous individual methods used for boron analysis for BNCT in clinical and biological samples are reported in detail. The main interferences of the analytical methods are described. Sample pretreatment techniques are discussed. The methods reviewed for boron analysis for BNCT concern atomic spectrometry, radioanalytical methods, and imaging techniques. An error analysis of boron determinations in biomaterials is performed and typical boron distribution patterns in small mammalians are discussed.
A critical comparison of on-line coupling IC-ICP-(AES, MS) with competing analytical methods for ultra trace analysis of microelectronic materials by Andreas Seubert (pp. 404-409).
On-line coupling of ion chromatography and atomic spectrometry (IC-ICP-(AES, MS)) are compared to so-called reference methods and other competing methods for ultra trace characterization of solid microelectronic materials. The comparison is based on analytical data gained for well characterized samples by a number of different laboratories. The matrices used for comparison are Mo, Mo-oxide, MoSix, W, W-oxide, WSix, metallic As, red P and Re. The analyte elements accessible by IC-ICP-(AES, MS) and with reference values for at least one other method are Ag, Al, Ba, Ca, Cd, Cr, Co, Cu, Fe, K, Mg, Mn, Na, Ni, Ti, Tl, Th, U and Zn. The agreement of results of IC-ICP-(AES, MS) with those of isotope dilution mass spectrometry (IDMS) and radiochemical activation analyses (RNAA) shows good accuracy for most elements and some contamination problems with ubiquitous elements. A correlation of IC-ICP-(AES, MS) and GDMS results is undoubtful, but the discrepancies are rather high. As further technique ETV-ICP-MS is compared, whose results are in reasonable agreement with IC-ICP-(AES, MS). Details on some new applications as well as of some new methodological enhancements of on-line coupling IC-ICP(AES, MS) for the matrices As and P were included.
Determination of trace impurities in high purity copper using sector-field ICP-MS: continuous nebulization, flow injection analysis and laser ablation by S. Pattberg; R. Matschat (pp. 410-416).
High resolution inductively coupled plasma mass spectrometry (HR-ICP-MS) was applied for multielement-determination in high-purity copper (approx. 99.99%). The samples were introduced into the instrument by three different introduction systems, which were studied with respect to high accuracy, low detection limits and fast analysis: continuous nebulization (CN), flow injection analysis (FIA) and laser ablation (LA). The trueness of the applied method was checked by the analysis of high-purity copper reference material (BCR Cu074). All values obtained for this CRM using CN were in the range of the stated uncertainty for the 9 elements determined: Ag, As, Bi, Cr, Fe, Ni, Pb, Sb, and Sn with contents in the range of 0.5–13 μg/g. Another approach for checking the trueness of the method was to compare the results obtained by this method characterizing the purity of a 4N (99.99% copper content) copper material with those obtained by application of electrothermal atomic absorption spectrometry (ET-AAS) and inductively coupled plasma optical emission spectrometry (ICP-OES). For further characterizing, the concentrations of 49 elements were found in this material below detection limits of HR-ICP-MS in the range of low μg/kg and sub μg/kg. The combination of HR-ICP-MS and a flow injection analysis system (FIAS) improved the robustness of the system in regard to high matrix concentrations. Therefore, matrix concentrations up to 4 g/L could be used for liquid analysis and detection limits were lowered by a factor of 2–5. A calibration method for bulk analysis with laser ablation was developed with doped copper powder as pressed pellets for calibration standards. This method proved to be an excellent fast semi-quantitative method, which was less time consuming in comparison with the analysis of liquids. After application of correction factors the deviation between the results obtained by laser ablation and by analysis of liquids was ≈ 15% for most elements. The method offered the possibility to check for potential losses of analytes occurring during the wet chemical operations.
Trace analysis of impurities in sol-gel prepared BaTiO3-powders with ICP-MS by W. Eiser; H. P. Beck (pp. 417-421).
An ICP-MS method for the determination of ultra-trace impurities of 21 elements (Be, Al, Ca, Cr, Mn, Co, Ni, Sr, Zr, Ag Cd, In, Sn, La, Ce, Er, Hf, W, Pb, Bi, U) at pg/g to ng/g level in BaTiO3-powders and precursors prepared by different sol-gel-methods was developed. The non-spectral matrix effects like suppression of the analyte signal and spectral effects like the formation of polyatomic ions like MO+, MAr+, MCl+ and M2+ which interfere with isotopes in isobar overlaps was investigated. To correct for these polyatomic ions a “blank solution” with the composition of the sample matrix was measured and the data were subtracted from the results of the sample; a standard addition method for calibration and 45Sc, 89Y, 103Rh and 141Pr as internal standards to compensate the matrix effects were used and improvements in accuracy and precision were shown. The stability of the instrument and the detection limits in the presence of the barium and titanium matrix were established. In BaTiO3 different amounts of trace impurities were detected in the μg/g to ng/g range. The main impurities are strontium and calcium. The source of the impurities are mainly the educts but it is shown that contamination during the synthesis process is also possible.
Determination of zirconium traces in polymers by ICP-IDMS – a powerful and fast method for routine testing of zirconium residues in polyolefins by Jürgen Diemer; Klaus G. Heumann (pp. 421-423).
Zirconium trace analyses play an important role for polyolefins produced by modern catalytic processes with zirconium metallocenes. A reliable and fast routine testing method by inductively coupled plasma isotope dilution mass spectrometry (ICP-IDMS) was therefore developed, which allows the determination of zirconium in polymers down to the low ng/g level. With respect to its precision, accuracy, and time-consumption this method is suitable for routine testing of production processes. A spike solution, enriched in the stable isotope 91Zr, was prepared and used for the isotope dilution procedure, which has the advantage of being an internal “one point” calibration method. The polyolefin samples were dissolved by microwave assisted digestion with a mixture of concentrated HNO3/HF.
Analysis of wines by ICP-MS: Is the pattern of the rare earth elements a reliable fingerprint for the provenance? by N. Jakubowski; R. Brandt; D. Stuewer; H. R. Eschnauer; S. Görtges (pp. 424-428).
In a comparative analysis of young and finished product wines by semi-quantitative ICP-MS, a striking difference was observed: finished products exhibited significant concentrations of the rare earth elements whereas the concentrations in young wines which had not been subdued to any treatment after their initial preparation from the grapes were below the determination limits with a quadrupole instrument and could only be determined with a magnetic field instrument operated at a low mass resolution (R = 300). The reason was found in contamination from bentonites as usually applied for the purification of wines from tarnishing components such as proteins. Therefore, bentonites of different origin were extracted with a reference wine, and an increase of the rare earth element concentrations by more than one order of magnitude was observed in the extracts. The investigation leads to the conclusion that the concentration pattern of the rare earth elements can be strongly affected by the wine producing process and therefore is not generally suitable as a fingerprint for the provenance of wines.
Investigations of trace elements in high salinity waters by ICP-MS by W. Klemm; G. Bombach; K. P. Becker (pp. 429-432).
A separation and enrichment procedure for the analysis of trace elements (Cd, Co, Cu, Fe, Mn, Ni, Pb, Tl, U, Zn) in seawater or brines from ore dumps by ICP-MS was established based on the complexation with sodium diethyldithiocarbamate-trihydrate (Na-DDTC) and separation on a phenyl column. The method was tested with seawater samples from the hydrothermal system of Axial Seamount, Juan de Fuca Ridge. The analytical results demonstrated the influence of hydrothermal activity on the concentration of Fe and Mn.
Determination of Li, Na, Mg, K, Ca and Fe with ICP-MS using cold plasma conditions by D. Wollenweber; Silke Straßburg; Gerold Wünsch (pp. 433-437).
Some important analytes in ICP-MS are interfered by plasma argon or argon species, such as ArO+ and 56Fe, 40Ar and K or Ca. One approach to overcome this interference is the use of reduced forward power and a metal shield inserted between torch and load coil. These so called cold plasma conditions reduce the background caused by argon species and the formerly interfered analytes can be easily detected in the ng/g-range. Other elements in the lower mass region also profit from these conditions even when they are not interfered in normal plasma mode. The limits of detection are improved due to reduced background noise level and enhanced ion transmission. On the other hand, the reduced power fed to the plasma lowers the analytical performance and makes it susceptible to matrix effects. Elements of higher mass generally show higher detection limits compared to normal plasma mode.
Measuring metal homogeneity in a matrix via the measurement of the ratio metal to matrix oxide using ICP-MS by Andrea Held; P. D. P. Taylor; Chris Ingelbrecht (pp. 437-439).
A simple method has been developed that allows a fast determination of the homogeneity of an element M in an alloy, even for minor components. This is done by measuring a ratio of ion currents I, I M/I M’O, whereby M’ is the matrix element, by inductively coupled plasma mass spectrometry (ICP-MS). The method can be used to determine the homogeneity of one component in a binary alloy and allows to estimate the sample size necessary to minimise uncertainty contributions due to inhomogeneity in the analysis of such an alloy. In this work the homogeneity of a niobium/0.1% zirconium alloy was determined on 1 mg samples. Accurate weighings of these small samples are not required, as the method is based on the measurement of the niobium/zirconium amount ratio in the dissolved samples. As this ratio is fairly large, the Zr/NbO amount ratio was measured instead to decrease the magnitude of the measured ratio. This ratio was found to be sufficiently stable over time for homogeneity testing. In this particular case the Zr/NbO ratio in the samples was found to vary by 0.049 relative for a 1 mg samples size.
Recent trends in trace element determination and speciation using inductively coupled plasma mass spectrometry by F. Vanhaecke; Luc Moens (pp. 440-451).
During the past decade, inductively coupled plasma mass spectrometry (ICPMS) has evolved from a delicate research tool, intended for the well-trained scientist only, into a more robust and well-established analytical technique for trace and ultra-trace element determination, with a few thousand of instruments used worldwide. Despite this immense success, it should be realized that in its ’standard configuration’– i.e. equipped with a pneumatic nebulizer for sample introduction and with a quadrupole filter – ICPMS also shows a number of important limitations and disadvantages: (i) the occurrence of spectral interferences may hamper accurate trace element determination, (ii) solid samples have to be taken into solution prior to analysis and (iii) no information on the ‘chemical form’ in which an element appears can be obtained. Self-evidently, efforts have been and still are made to overcome the aforementioned limitations to the largest possible extent. The application of a double focusing sector field mass spectrometer in ICPMS instrumentation offers a higher mass resolution, such that spectral overlap can be avoided to an important extent. Additionally, in a sector field instrument, photons are efficiently eliminated from the ion beam, resulting in very low background intensities, making it also very well-suited for extreme trace analysis. Also the combination of the ICP as an ion source and a quadrupole filter operated in a so-called ‘alternate’ stability region, an ion trap or a Fourier transform ion cyclotron resonance mass spectrometer allows high(er) mass resolution to be obtained. With modern quadrupole-based instruments, important types of spectral interferences can be avoided by working under ‘cool plasma’ conditions or by applying a collision cell. The use of electrothermal vaporization (ETV) or especially laser ablation (LA) for sample introduction permits direct analysis of solid samples with sufficient accuracy for many purposes. The application range of LA-ICPMS has become very wide and the introduction of UV lasers has led to an improved spatial resolution. Solid sampling ETV-ICPMS on the other hand can be used for some specific applications only, but accurate calibration is more straightforward than with LA-ICPMS. Limited multi-element capabilities, resulting from the transient signals observed with ETV or single shot LA, can be avoided by the use of a time-of-flight (TOF) ICPMS instrument. Finally, when combined with a powerful chromatographic separation technique, an ICP-mass spectrometer can be used as a highly sensitive, element-specific multi-element detector in elemental speciation studies. Especially liquid (HPLC-ICPMS) and – to a lesser extent – gas (GC-ICPMS) chromatography have already been widely used in combination with ICPMS. In speciation work, sample preparation is often observed to be troublesome and this aspect is presently receiving considerable attention. For GC-ICPMS, new sample pretreatment approaches, such as headspace solid phase microextraction (headspace SPME) and the purge-and-trap technique have been introduced. Also supercritical fluid chromatography (SFC) and capillary electrophoresis (CE) show potential to be of use in combination with ICPMS, but so far the application ranges of SFC-ICPMS and CE-ICPMS are rather limited. It is the aim of the present paper to concisely discuss the aforementioned recent ’trends’ in ICPMS, using selected real-life applications reported in the literature.
A new interface for combining capillary electrophoresis with inductively coupled plasma-mass spectrometry by Dirk Schaumlöffel; A. Prange (pp. 452-456).
This paper describes the development and design of a new, efficient, simple and robust interface for coupling capillary electrophoresis (CE) with inductively coupled plasma-mass spectrometry. The interface is based on a modified microconcentric nebulizer which permits a low flow rate of about 6 μL/min in the free aspiration mode. This interface construction provides an electrical connection for stable electrophoretic separations and adapts the flow rate of the electro-osmotic flow inside the CE capillary to the flow rate of the nebulizer for efficient transport of the analytes into the plasma. By optimization of the fluid mechanical properties the interface prevents the nebulizer from causing any laminar flow in the CE capillary and thus the high resolution power of CE can be preserved. Furthermore, this new device permits independent optimization of the nebulization from the CE whereby exact positioning of the CE capillary is not necessary, thus enabling fast exchange. A low dead volume spraychamber has been constructed which circumvents any band broadening of the sharp CE signals. Peak widths down to 3.5 s comparable to CE with UV detection are possible.
Speciation of trace amounts of aluminium in percolating water of forest soil by online coupling HPLC-ICP-MS by A. Hils; M. Grote; E. Janßen; J. Eichhorn (pp. 457-461).
Procedures were developed for the speciation of trace amounts of aluminium present in percolating water of forest soil by online coupling of different chromatographic separation methods to an ICP-MS detection system. Inorganic and organic aluminium species were fractionated on a cation exchange column IONPAC CG12 (10-32). Phytotoxic polymeric aluminium hydroxides, as e.g. Al13 (AlO4Al12(OH)24(H2O)12 7+), were determined using pyrocatechol violet (PCV) as a species dependant complexing reagent prior to the cation exchange step. Size fractionation of the organic aluminium species was obtained by size exclusion chromatography using the columns Superdex-75-HR 10/30 and Superdex-Peptide-HR 10/30. Validation of the speciation procedures proved that online coupling HPLC to the element selective and sensitive ICP-MS detection system leads to low detection limits of 0.3–0.6 μg/L and high precision and reproducibility (1.2–3.5%) of the speciation procedures. Speciation data determined for aluminium in a percolating water of the Zierenberg catchment are given.
Simultaneous determination of arsenic, selenium and antimony species using HPLC/ICP-MS by T. Lindemann; A. Prange; W. Dannecker; B. Neidhart (pp. 462-466).
A new method for the simultaneous separation and determination of four arsenic species [As(III), As(V), monomethylarsonic acid and dimethylarsinic acid], three selenium species [Se(IV), Se(VI) and selenomethionine] as well as Sb(III) and Sb(V) is presented. The speciation was achieved by on-line coupling of anion exchange high-performance liquid chromatography (HPLC) with inductively coupled plasma mass spectrometry (ICP-MS). Chromatographic parameters such as the composition and pH of the mobile phase were optimised. Limits of detection are below 4.5 μg L–1 (as element) for Sb(III) and the selenium species and below 0.5 μg L–1 for the other species. Precisions of retention times were better than 2% RSD and of peak areas better than 8% RSD for all the species investigated.
Speciation of arsenic of liquid and gaseous emissions from soil in a microcosmos experiment by liquid and gas chromatography with inductively coupled plasma mass spectrometer (ICP-MS) detection by T. Prohaska; M. Pfeffer; M. Tulipan; G. Stingeder; A. Mentler; W. W. Wenzel (pp. 467-470).
Gas chromatography and high-performance liquid chromatography coupled to a double focusing sectorfield ICP-MS as sensitive element specific detector are used for the speciation of arsenic of liquid and gaseous emissions from soil samples, which were equilibrated in a microcosmos experiment. Speciation of liquid samples was performed by HPLC and hydride generation was used as introduction system to ICP-MS. An online prereduction step was introduced to enhance the sensitivity for As(V). A home-built and laboratory-ready transfer line from GC to ICP-MS is presented and quantification of As in gaseous emissions was performed by external calibration via hydride generation. The microcosmos experiment revealed only low production rates of organoarsenic compounds and reflected a limited capability of the biovolatilization experiment for the simulation of natural systems.
Recent developments in and applications of resonance ionization mass spectrometry by K. Wendt; K. Blaum; B. A. Bushaw; C. Grüning; R. Horn; G. Huber; J. V. Kratz; P. Kunz; P. Müller; W. Nörtershäuser; M. Nunnemann; G. Passler; A. Schmitt; N. Trautmann; A. Waldek (pp. 471-477).
Resonance Ionization Mass Spectrometry (RIMS) has nowadays reached the status of a routine method for sensitive and selective ultratrace determination of long-lived radioactive isotopes in environmental, biomedical and technical samples. It provides high isobaric suppression, high to ultra-high isotopic selectivity and good overall efficiency. Experimental detection limits are as low as 106 atoms per sample and permit the fast and sensitive determination of ultratrace amounts of radiotoxic contaminations. Experimental arrangements for the detection of different radiotoxic isotopes, e.g. 236–244Pu, 89,90Sr and 99Tc in environmental samples are described, and the application of RIMS to the ultrarare long-lived radioisotope 41Ca for cosmochemical, radiodating and medical purposes are presented.
Magnesium isotope ratio measurements by negative thermal ionisation mass spectrometry using molecular fluoride ions by S. Richter; M. Berglund; C. Hennessy (pp. 478-481).
A new technique for accurate Mg isotope ratio measurements has been developed with MgF2 as sample compound. With the help of a fluorinating agent negatively charged MgF3 molecular ions were formed in the ion source of a thermal ionisation mass spectrometer. An evaporation study has been performed and the results clearly show that Mg is evaporated from the filament as MgF2 molecules. The MgF2 technique has been applied in the certification of a candidate 26Mg-enriched Spike Isotope Reference Material. The result from this new technique has been compared with results obtained for the same material using ICP-MS.
Precise isotope ratio measurements for uranium, thorium and plutonium by quadrupole-based inductively coupled plasma mass spectrometry by J. S. Becker; Hans-Joachim Dietze (pp. 482-488).
Precise long-term measurements of uranium and thorium isotope ratios was carried out in 1 μg/L solutions using a quadrupole inductively coupled plasma mass spectrometer (ICP-QMS). The isotopic ratios of uranium (235U/ 238U = 1, 0.02 and 0.00725) were determined using a cross-flow nebulizer (CFN, at solution uptake rate of 1 mL/min) and a low-flow microconcentric nebulizer (MCN, at solution uptake rate of 0.2 mL/min) over 20 h. For 1 μg/L uranium solution (235U/238U = 1) relative external standard deviations (RESDs) of 0.05% and 0.044% using CFN and MCN, respectively, can be achieved. Additional short term isotope ratio measurements using a direct injection high-efficiency nebulizer (DIHEN) of 1 μg/L uranium solution (235U/238U = 1) at a solution uptake rate of 0.1 mL/min yielded an RSD of 0.06–0.08%. The sensitivity of solution introduction by DIHEN for uranium, thorium and plutonium (145 MHz/ppm, 150 MHz/ppm and 177 MHz/ppm, respectively) increased significantly compared to CFN and MCN and the solution uptake rate can be reduced to 1 μL/ min in DIHEN-ICP-MS. Isotope ratio measurements at an ultralow concentration level (e.g. determination of 240Pu/ 239Pu isotope ratio in a 10 ng/L Pu waste solution) were carried out for the characterization of radioactive waste and environmental samples.
Mass spectrometric investigations of the kinetic stability of chromium and copper complexes with humic substances by isotope-labelling experiments by Giselher Marx; K. G. Heumann (pp. 489-494).
Isotope-labelling exchange experiments were carried out to investigate the kinetic stability of Cr(III) complexes with humic substances (HS). To compare the results with those of an ion, not expected to form kinetically stable HS complexes with respect to its electron configuration, Cu(II) was investigated under the same conditions. HS solutions of different origin were therefore spiked with 53Cr(III) or 65Cu(II) after saturation of HS with chromium and copper of natural isotopic composition. In fractions of metal/HS complexes with different molecular weight, obtained by ultrafiltration and HPLC/ICP-MS using size exclusion chromatography (SEC), respectively, the isotope ratios of chromium and copper were determined by ICP and thermal ionisation mass spectrometry. Distinct differences in the isotopic composition of chromium were found in the permeate of the ultrafiltration compared with the corresponding unseparated solution, which indicates kinetically stable Cr(III)/HS complexes. On the other hand, the copper isotopic composition was identical in the permeate and the unseparated solution, which shows that a total exchange of Cu2+ ions took place between free and HS complexed copper ions. The SEC/ ICP-MS experiments also resulted in a different isotopic distribution of chromium in the chromatographically separated complexes whereas the copper complexes, separated by SEC, showed identical isotopic composition. The kinetic stability of Cr(III)/HS complexes could be explained by the d3 electron configuration of Cr3+ ions, a fact which is well known from classical Cr(III) complexes, and influences substantially the mobility of this heavy metal in the environment.
Strategies for isotope ratio measurements with a double focusing sector field ICP-MS by M. Hamester; D. Wiederin; J. Wills; W. Kerl; C. B. Douthitt (pp. 495-498).
A single collector double focusing sector field ICP-MS is evaluated for the determination of isotope ratios. Spectral interferences (e.g. 40Ar23Na on 63Cu) can lead to calculation of inaccurate ratios. The use of high resolution enables such interferences to be separated from the isotopes of interest. External reproducibilities of < 0.02% are shown for uninterfered isotopes (measured at low resolution R = 300) and < 0.1% for interfered isotopes which required the use of medium (R = 4000) and high resolution (R = 10000).